Recycle of random sequences
Nobuyasu Ito, Macoto Kikuchi, Yutaka Okabe

TL;DR
This paper investigates how permutation transformations affect the correlation of random sequences, demonstrating that shuffling can produce sequences nearly independent, with applications to Monte Carlo simulations, notably in Ising models.
Contribution
It introduces a method to analyze and reduce correlation in random sequences through permutation, enhancing Monte Carlo simulation accuracy.
Findings
Permutation can make sequences nearly independent
Shuffling reduces correlation significantly
Applicable to Ising Monte Carlo simulations
Abstract
The correlation between a random sequence and its transformed sequences is studied. In the case of a permutation operation or, in other word, the shuffling operation, it is shown that the correlation can be so small that the sequences can be regarded as independent random sequences. The applications to the Monte Carlo simulations are also given. This method is especially useful in the Ising Monte Carlo simulation.
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